Segment Tree Build

The structure of Segment Tree is a binary tree which each node has two attributes start and end denote an segment / interval.

start and end are both integers, they should be assigned in following rules:

• The root's start and end is given by build method.
• The left child of node A has start=A.left, end=(A.left + A.right) / 2.
• The right child of node A has start=(A.left + A.right) / 2 + 1, end=A.right.
• If start equals to end, there will be no children for this node.

Implement a build method with two parameters start and end, so that we can create a corresponding segment tree with every node has the correct start and end value, return the root of this segment tree.

Example

Given start=0, end=3. The segment tree will be:

            [0,  3]
          /        \
   [0,  1]           [2, 3]
   /     \           /     \
[0, 0]  [1, 1]     [2, 2]  [3, 3]

Given start=1, end=6. The segment tree will be:

               [1,  6]
             /        \
       1,  3]           [4,  6]
      /     \           /     \
   [1, 2]  [3,3]     [4, 5]   [6,6]
   /    \           /     \
[1,1]   [2,2]     [4,4]   [5,5]

Clarification

Segment Tree (a.k.a Interval Tree) is an advanced data structure which can support queries like:

• which of these intervals contain a given point
• which of these points are in a given interval

Complexity

Time: O(n), at most 2n - 1 nodes

Space: O(h), recursion depth

Code

Java

/**
 * Definition of SegmentTreeNode:
 * public class SegmentTreeNode {
 *     public int start, end;
 *     public SegmentTreeNode left, right;
 *     public SegmentTreeNode(int start, int end) {
 *         this.start = start, this.end = end;
 *         this.left = this.right = null;
 *     }
 * }
 */
public class Solution {
  /**
   *@param start, end: Denote an segment / interval
   *@return: The root of Segment Tree
   */
  public SegmentTreeNode build(int start, int end) {
    if (start > end) {
      return null;
    } else if (start == end) {
      return new SegmentTreeNode(start, end);
    }
    int mid = start + (end - start) / 2;
    SegmentTreeNode root = new SegmentTreeNode(start, end);
    root.left = build(start, mid);
    root.right = build(mid + 1, end);
    return root;
  }
}